# Geometry: Identifying the Cube

A cube is a 3-D closed figure formed by 6 square faces joined along their edges. Thus all the edges of a cube are equal in length. Also, the areas of all faces of cube are also same. The cube is also called a regular hexahedron.

**Parts of a cube:**

**Face: **A cube is forms by 6 square each of which is called the face of the cube.

**Edge:** Each face of a cube is a square which has 4 sides each of which is called an edge.So there will be totally 12 edges in a cube.

**Vertex: **A point at which 3 edges meet is called the vertex of the cube. So, there will be 8 vertices in a cube.

**Face diagonal: **Face diagonal is a line segment joining the opposite corners of the face. Since there are 6 faces each with 2 diagonals, there are totally 6×2 = 12 face diagonals.

**Space diagonals: **A space diagonal is a line segment which joins the opposite corners of the cube cutting the interior. So there are 4 space diagonals in a cube.

**Surface area of a cube:**

The surface of the cube is contains 6 squares. So if ** a** is the edge of each square then the area of each square is a

^{2}. So the surface area of the cube is 6 times the area of each of the square.

So, ** surface area of the cube = 6a^{2}**.

**Volume of a cube:**

The volume of a prism is nothing but the product of area of its base and its height. A cube is also a prism whose base is a square and height is same as the side length of the square.

If ** a** is the edge of each square then the area of each square is a

^{2}. So the area of the base is a

^{2}.

So, *volume of the cube = a ^{2} x a = a^{3}.*

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